Adaptive Optics (AO) is a technology which allows to compensate for the rapidly changing optical distortions arising during the imaging process. In ground-based telescopes, the light coming from the astronomical objects is being distorted by the turbulent nature of the atmosphere caused by, e.g., changing temperature and wind conditions. Adaptive optics is used in large scale telescope imaging in order to enhance the resolution of the images and to avoid costly post-processing. Equipped with the AO correction, the large ground-based telescopes are able to compete with the space telescopes with respect to the accuracy of the reconstruction.

The AO mechanism is based on the measurements of the wavefront aberration and produces commands which are applied to deformable mirrors that correct the aberration. However, the correction should be fast enough, in order to keep up with the rapidly changing atmosphere. Fast computation of the corrections from a huge amount of the censored data with acceptable quality is one challenge in the modern AO technology. Another important issue is the fact that, for a larger field of view, the mathematical model which describes the correction process becomes ill-posed. In practice, it means that small errors arising in the measurement process may cause arbitrarily large discrepancies in the obtained corrections, making them unusable. In order to overcome the negative effects of the ill-posedness, sophisticated methods from the field of inverse problems, such as regularization, have to be applied.